What do the settings in the new Principled Shader actually do?
Most of these answers can be dug out of the paper linked by timaroberts


The default specular of 0.5 corresponds to an IOR of 1.5. See section 5.4 of the paper: 



  In place of an explicit index-of-refraction, or ior, our specular parameter determines the incident
  specular amount. The normalized range of this parameter is remapped linearly to the incident specular
  range [0.0, 0.08]. This corresponds to ior values in the range [1.0, 1.8], encompassing most common
  materials. Notably, the middle of the parameter range corresponds to an ior of 1.5, a very typical
  value, and is also our default. The specular parameter may be pushed beyond one to reach higher ior
  values but should be done with caution. This mapping of the parameter has helped greatly in getting artists to make plausible materials given that real-world incident reflectance values are so unintuitively
  low.



(cont) Note that this is different from PBR spec/gloss shaders, which directly map the incident specular (the 0.0 - 0.08) values mentioned in the above paragraph. "Specular" outputs from software such as Substance should NOT be connected to this input, they contain different data entirely. Cycles' fresnel node uses a default IOR of 1.45 instead of 1.5, so it will have a slightly different look by default. Both 1.45 and 1.5 were chosen for being nice round numbers in the rough ballpark of most dielectrics, so neither is necessarily right or wrong as the default. Worth noting the viewport shader in Substance does not allow editing of this setting and just locks it off at 0.5, so if you want to match Substance, you should not modify this value.
See section 4.5 of the Disney paper. It pushes up the specular component at grazing angles to approximate light interacting with cloth fibers. It adds some extra off-angle sheen similar to Cycles' velvet shader
Since the light diffusing through cloth will pick up the color of the cloth, there's an option, sheen tint, to tint the extra spec with the base color. Since this is useful in many cases, it defaults to 0.5 so it is auto-enabled when sheen is enabled.
To be honest, I have no idea why this was done. Some other PBR shaders, such as Arnold's aiStandardSurface, still use roughness for clearcoat. Likely it made sense to someone at Disney working on the shader and they just ran with it. They didn't bother to record their reasoning in the original paper that I can find.
The paper mentions they used clearcoat normals to get some floor sparkle effects in Wreck It Ralph. Also, since the clearcoat normal is independent (to allow things like carbon fiber as you mentioned), you still need some ability to set it when you DO want your base normals to also apply to the clearcoat. In this case you aren't really applying a different normal, you'd just connect the same bump/normal node to both inputs, but you need the separate input so you have the option to NOT apply the bump/normal map to the clearcoat.